There is growing interest in employing robotic manipulators to perform assembly tasks. In particular, space robots have become a viable means to perform extravehicular robotic tasks. For instance, the Special Purpose Dextrous Manipulator (SPDM) will be used to handle various orbital replacement units (ORU) for the maintenance operations of the International Space Station.
The complexity of a robotic operation associated with a task demands verification facility on the ground to ensure that the task can be performed on orbit as intended. This requirement has motivated the development of the SPDM task verification facility at Canadian Space Agency. The verification operation on the ground is challenging as space robots are designed to work only in micro-gravity environment. In reality, thanks to weightlessness on orbit, the SPDM can handle payloads as massive as 600 kg. On the ground, however, it cannot even support itself against gravity. Although this problem could be fixed by using a system of weights and pulleys to counterbalance gravity, the weights change the robot inertia and its dynamical, behavior. Moreover, it is difficult to replicate the dynamical effects induced by the flexibility of the space robot or space structure on which the manipulator is stowed.
Simulation is another tool that can be used to validate the functionality of a space manipulator. Although the dynamics and kinematics models of space manipulators are more complex than those of terrestrial manipulators due to dynamic coupling between the manipulator and its spacecraft, the space-robot dynamics can be captured by the concept of a Virtual-Manipulator, which has a fixed base in inertial space at a point called Virtual Ground. Today, with the advent of powerful computers, faithful and real-time simulators are available that can capture dynamics of almost any type of manipulator with many degrees of freedom. However, simulation of a robot interacting with environment with a high fidelity requires accurate modeling of both the manipulator and the contact interface between the manipulator and its environment. Faithful models of space-robots are available; it is the calculation of the contact force which poses many technical difficulties associated with contact dynamics.
In the literature, many models for the contact force, consisting of normal and friction forces, have been reported. The Hertz contact theory is used to estimate local forces. However, to predict where the contact points are, calls to an optimization routine, thus demanding substantial computational effort. In particular, the complexity of contact-dynamics modelling tends to increase exponentially when the two objects have multi-point contacts. Moreover, since the SPDM is tele-operated by a human operator, the validation process requires inclusion of a real-time simulation environment since the simulation should allow human operators to drive the simulation in real-time.
The greatest challenge in the control of robots interacting with an unknown environment is to establish a desired impedance characteristic while maintaining stability of the contact between the robot and the environment. Typically, the parameters of the impedance controller, i.e., desired mass, damping and stiffness matrices, are tuned by trial-and-error to achieve stability and a satisfactory performance. This is not effective because the performance is not optimal and control parameters are valid only for a particular environment; they often need to be changed as the environment changes.
Impedance control is suitable for robotic tasks such as assembly or insertion operations to avoid jamming among parts. The impedance captures the dynamical relation between position and force of a robot's end-effector. The underlying idea of impedance control is to assign a prescribed dynamic behavior for a robot manipulator while its end-effector is interacting with the environment. It is known that any assigned impedance may not lead to contact stability even if the desired impedance per se is stable. In practice, the parameters of the impedance controller, i.e., desired mass, damping and stiffness matrices, are tuned by trial-and-error to achieve stability and a satisfactory performance. Typically, the control parameters are valid for a particular environment and they often need to be changed as the environment changes.
The impedance control of a robot to shape the robot force-response was proposed by Hogan, “Impedance Control: An approach to manipulation”, Journal of Dynamics, Measurement, and Control, vol. 107, pp. 8-16, 1985, the contents of which are herein incorporated by reference. In his approach the force is virtually controlled by controlling position by using programmable stiffness and damping matrices in the impedance model. Analysis and general methodology for implementation of attaining the desired impedance have been the focus of many other research works. All control approaches are based on the premise that a perfect model of the manipulator and ideal source of joint torque, i.e., no actuator dynamics, are available and that the robot is rigid. Therefore, the control system can trivially assign infinite stiffness to the manipulator and then the desired impedance of the target robot can be achieved by cascading the transfer function of desired impedance model.
In practice, the robot prototype has a finite bandwidth and stiffness that impose a serious limitation on the impedance that can be attained in a stable manner. In other words, the conventional impedance control methodology does not guarantee that a passive mechanical admittance will result from the design and hence contact instability may occur for a class of environment impedance. Also, the conventional impedance approach doesn't allow a generic desired-impedance; only the second order system of mass-spring-damper is allowed.